The disruption -- Capital assembled -- Capital goes to work -- Capital goes to market -- Capital evolves -- The geography of it all -- Creative destruction on the land -- What is to be done? And who is going to do it?

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.

Theories and Methods is the one compulsory unit on the AEB and Interboard syllabuses. This guide outlines the main sociological perspectives, and discusses three main approaches: positivism, phenomenology and critical social research. The topic-book format should be suitable for linear and modular courses, and there are sample questions and skills advice.

In the Foundational Life, philosophy is commonly used as a method for choosing and analyzing fundamental concepts, and mathematics is commonly used for rigorous development. The mathematics informs the philosophy and the philosophy informs the mathematics.

Many years ago Wilamowitz desiderated a systematic collection of the texts which relate to the different types of poetry composed by the great lyric poets of Greece. He hoped that if we could only crystallize our admittedly scanty information about the characteristics of, say, the Paean or the Dirge, we might be able to reach a slightly better understanding than we have now of the formal structure and artistic design of the poems and fragments which have come down to us (...) under these titles. Indeed, this kind of knowledge is very important. (shrink)

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

This paper responds to Kauffeld’s 2009 OSSA paper, considering the adequacy of his “commitment-based” approach to “ordinary presumptive practices” to sup-ply an account of presumption fit for general application in normative theories of argument. The central issue here is whether socially-grounded presumptions are defeasible in the right sorts of ways so as to pro-duce “truth-tropic” presumptive inferences.

This essay argues that it is a matter of vital concern to develop a theoretical apparatus that is adequate to the inherent spatiotemporal dynamics of capital accumulation and the changing practices developed to manage the crisis tendencies of those dynamics. This requires integrating the a-spatial theory of capital accumulation and its internal contradictions with the spatial/geographical theory of imperialism that invokes geopolitical and geo-economic struggles between nation-states. I argue that the two are linked by the way capital deals with the (...) problem of absorbing capital surpluses, namely through geographical fixes. The geographical fix requires imperialist expansionism and the battering down of all barriers to the spatial movement of capital. Such a conception provides the necessary clarity in formulating the relations between capital and state that are sometimes missing from Ellen M. Wood's arguments in Empire of Capital. (shrink)

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic.

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

Gödel's definitive results and his essays leave us with a rich legacy of philosophical programs that promise to be subject to mathematical treatment. After surveying some of these, we focus attention on the program of circumventing his demonstrated impossibility of a consistency proof for mathematics by means of extramathematical concepts.

S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, S. (...) Thomas, A. Valette, V.S. Varadarajan, B. Velickovic, B. Weiss, J.D.M. Wright, R.J. Zimmer. (shrink)

For digraphs G, we write V(G) for the set of all vertices of G, and E(G) for the set of all edges of G. A digraph on a set E is a digraph G where V(G) = E.

The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.

This distinction between logic and mathematics is subject to various criticisms and can be given various defenses. Nevertheless, the division seems natural enough and is commonly adopted in presentations of the standard foundations for mathematics.

We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert's Tenth Problem. The limited number of facts used from recursion theory are isolated at the beginning.

Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.

One of the ways in which a poet may show his quality is by discrimination and originality in his choice of adjectives. Poetry likes to adorn the bare noun; a noun such as ‘the sky’ calls out for an attribute. But in practice the poet has to take care to avoid the cliche. He can seldom write ‘the blue sky’; even ‘the azure sky’ has become trite. He has to search for the epithet which will be both apt and original.

To prove this, we fix P(x) to be any polynomial of degree ≥ 1 with a positive and negative value. We define a critical interval to be any nonempty open interval on which P is strictly monotone and where P is not strictly monotone on any larger open interval. Here an open interval may not have endpoints in F, and may be infinite on the left or right or both sides. Obviously, the critical intervals are pairwise disjoint.

In this paper, I shall argue that Dissociative Identity Disorder (DID), a disorder in which seemingly independent identities (alters) arise within the same individual, can have considerable consequences in Christian theology. I shall focus on traditional Christian understandings of the afterlife. I shall begin by outlining DID, and shall argue that in some DID cases, alters appear to be different persons according to some definitions of personhood in Christian theology. I shall then illustrate the difficulty this raises for two influential (...) ideas in the Christian tradition: the heaven and hell understanding of the afterlife, and the idea of the resurrection of the body. Finally, I shall consider some objections to the problem, and shall highlight which responses are the most plausible. (shrink)

(1995). Innovation and change in the production of knowledge. Social Epistemology: Vol. 9, Knowledge (EX) Change, pp. 211-232. doi: 10.1080/02691729508578789.

Philosopy of medicine focuses inter alia on metaphysics and epistemology that are instantiated in biomedicine as physicalism (or materialism) and empiricism. The Golubchuck case reveals how the clinicans failed to recognize the relation between medical science and medical ethics and made biomedical decsions devoid of medical ethics. That is, they failed to make medical judgments that by defintion include a normative ethical component.

While intended more for intellectual historians than for philosophers or Harvardians, this book will be found valuable by all three of these groups, hitherto considered distinct. The author announces three themes: the Harvard curriculum of moral philosophy in the seventeenth century; the transition in that century from scholasticism to Cartesianism, as visible in the great change in Harvard texts from 1650 to 1710; and a more specific argument that the influence of eighteenth-century sentimentalism was prepared by seventeenth-century Puritan religious thought. (...) These themes are articulated in chapters that are roughly chronological and show the stages of the critical transition, or change, from Aristotle to modern moral philosophy. One should note that Fiering has also produced a sequel to this book, Jonathan Edwards's Moral Thought and Its British Context, with the same publisher. (shrink)

We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of as a (...) (rather weak) sort of $L_{\omega_1\omega}$-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields. (shrink)

Harvey Mitchell’s book argues that a reassessment of Voltaire’s treatment of traditional Judaism will sharpen discussion of the origins of, and responses to, the Enlightenment. His study shows how Voltaire’s nearly total antipathy to Judaism is best understood by stressing his self-regard as the author of an enlightened and rational universal history, which found Judaism’s memory of its past incoherent, and, in addition, failed to meet the criteria of objective history—a project in which he failed. Calling on an array (...) of Jewish and non-Jewish figures to reveal how modern interpretations of Judaism may be traced to the core ideas of the Enlightenment, this book concludes that Voltaire paradoxically helped to foster the ambiguities and uncertainties of Judaism’s future. (shrink)

Writing for a wide audience, Harvey here tells the political-economic story of where neoliberalization came from and how it proliferated on the world stage. He constructs a framework, not only for analyzing the political and economic dangers that now surround us, but also for assessing the prospects for more socially just alternatives.